/**
 * @license
 * Copyright (c) 2013, Brandon Jones, Colin MacKenzie IV. All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are met:
 *
 *   * Redistributions of source code must retain the above copyright notice,
 * this list of conditions and the following disclaimer.
 *   * Redistributions in binary form must reproduce the above copyright notice,
 * this list of conditions and the following disclaimer in the documentation
 * and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
 * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
 * POSSIBILITY OF SUCH DAMAGE.
 */

import { GLMAT_ARRAY_TYPE } from './common';
import vec3 from './vec3';
import vec4 from './vec4';
import mat3 from './mat3';


/**
 * @class Quaternion
 * @name quat
 */

var quat = {};

/**
 * Creates a new identity quat
 *
 * @returns {quat} a new quaternion
 */
quat.create = function() {
    var out = new GLMAT_ARRAY_TYPE(4);
    out[0] = 0;
    out[1] = 0;
    out[2] = 0;
    out[3] = 1;
    return out;
};

/**
 * Sets a quaternion to represent the shortest rotation from one
 * vector to another.
 *
 * Both vectors are assumed to be unit length.
 *
 * @param {quat} out the receiving quaternion.
 * @param {vec3} a the initial vector
 * @param {vec3} b the destination vector
 * @returns {quat} out
 */
quat.rotationTo = (function() {
    var tmpvec3 = vec3.create();
    var xUnitVec3 = vec3.fromValues(1,0,0);
    var yUnitVec3 = vec3.fromValues(0,1,0);

    return function(out, a, b) {
        var dot = vec3.dot(a, b);
        if (dot < -0.999999) {
            vec3.cross(tmpvec3, xUnitVec3, a);
            if (vec3.length(tmpvec3) < 0.000001)
                vec3.cross(tmpvec3, yUnitVec3, a);
            vec3.normalize(tmpvec3, tmpvec3);
            quat.setAxisAngle(out, tmpvec3, Math.PI);
            return out;
        } else if (dot > 0.999999) {
            out[0] = 0;
            out[1] = 0;
            out[2] = 0;
            out[3] = 1;
            return out;
        } else {
            vec3.cross(tmpvec3, a, b);
            out[0] = tmpvec3[0];
            out[1] = tmpvec3[1];
            out[2] = tmpvec3[2];
            out[3] = 1 + dot;
            return quat.normalize(out, out);
        }
    };
})();

/**
 * Sets the specified quaternion with values corresponding to the given
 * axes. Each axis is a vec3 and is expected to be unit length and
 * perpendicular to all other specified axes.
 *
 * @param {vec3} view  the vector representing the viewing direction
 * @param {vec3} right the vector representing the local "right" direction
 * @param {vec3} up    the vector representing the local "up" direction
 * @returns {quat} out
 */
quat.setAxes = (function() {
    var matr = mat3.create();

    return function(out, view, right, up) {
        matr[0] = right[0];
        matr[3] = right[1];
        matr[6] = right[2];

        matr[1] = up[0];
        matr[4] = up[1];
        matr[7] = up[2];

        matr[2] = -view[0];
        matr[5] = -view[1];
        matr[8] = -view[2];

        return quat.normalize(out, quat.fromMat3(out, matr));
    };
})();

/**
 * Creates a new quat initialized with values from an existing quaternion
 *
 * @param {quat} a quaternion to clone
 * @returns {quat} a new quaternion
 * @function
 */
quat.clone = vec4.clone;

/**
 * Creates a new quat initialized with the given values
 *
 * @param {Number} x X component
 * @param {Number} y Y component
 * @param {Number} z Z component
 * @param {Number} w W component
 * @returns {quat} a new quaternion
 * @function
 */
quat.fromValues = vec4.fromValues;

/**
 * Copy the values from one quat to another
 *
 * @param {quat} out the receiving quaternion
 * @param {quat} a the source quaternion
 * @returns {quat} out
 * @function
 */
quat.copy = vec4.copy;

/**
 * Set the components of a quat to the given values
 *
 * @param {quat} out the receiving quaternion
 * @param {Number} x X component
 * @param {Number} y Y component
 * @param {Number} z Z component
 * @param {Number} w W component
 * @returns {quat} out
 * @function
 */
quat.set = vec4.set;

/**
 * Set a quat to the identity quaternion
 *
 * @param {quat} out the receiving quaternion
 * @returns {quat} out
 */
quat.identity = function(out) {
    out[0] = 0;
    out[1] = 0;
    out[2] = 0;
    out[3] = 1;
    return out;
};

/**
 * Sets a quat from the given angle and rotation axis,
 * then returns it.
 *
 * @param {quat} out the receiving quaternion
 * @param {vec3} axis the axis around which to rotate
 * @param {Number} rad the angle in radians
 * @returns {quat} out
 **/
quat.setAxisAngle = function(out, axis, rad) {
    rad = rad * 0.5;
    var s = Math.sin(rad);
    out[0] = s * axis[0];
    out[1] = s * axis[1];
    out[2] = s * axis[2];
    out[3] = Math.cos(rad);
    return out;
};

/**
 * Adds two quat's
 *
 * @param {quat} out the receiving quaternion
 * @param {quat} a the first operand
 * @param {quat} b the second operand
 * @returns {quat} out
 * @function
 */
quat.add = vec4.add;

/**
 * Multiplies two quat's
 *
 * @param {quat} out the receiving quaternion
 * @param {quat} a the first operand
 * @param {quat} b the second operand
 * @returns {quat} out
 */
quat.multiply = function(out, a, b) {
    var ax = a[0], ay = a[1], az = a[2], aw = a[3],
        bx = b[0], by = b[1], bz = b[2], bw = b[3];

    out[0] = ax * bw + aw * bx + ay * bz - az * by;
    out[1] = ay * bw + aw * by + az * bx - ax * bz;
    out[2] = az * bw + aw * bz + ax * by - ay * bx;
    out[3] = aw * bw - ax * bx - ay * by - az * bz;
    return out;
};

/**
 * Alias for {@link quat.multiply}
 * @function
 */
quat.mul = quat.multiply;

/**
 * Scales a quat by a scalar number
 *
 * @param {quat} out the receiving vector
 * @param {quat} a the vector to scale
 * @param {Number} b amount to scale the vector by
 * @returns {quat} out
 * @function
 */
quat.scale = vec4.scale;

/**
 * Rotates a quaternion by the given angle about the X axis
 *
 * @param {quat} out quat receiving operation result
 * @param {quat} a quat to rotate
 * @param {number} rad angle (in radians) to rotate
 * @returns {quat} out
 */
quat.rotateX = function (out, a, rad) {
    rad *= 0.5;

    var ax = a[0], ay = a[1], az = a[2], aw = a[3],
        bx = Math.sin(rad), bw = Math.cos(rad);

    out[0] = ax * bw + aw * bx;
    out[1] = ay * bw + az * bx;
    out[2] = az * bw - ay * bx;
    out[3] = aw * bw - ax * bx;
    return out;
};

/**
 * Rotates a quaternion by the given angle about the Y axis
 *
 * @param {quat} out quat receiving operation result
 * @param {quat} a quat to rotate
 * @param {number} rad angle (in radians) to rotate
 * @returns {quat} out
 */
quat.rotateY = function (out, a, rad) {
    rad *= 0.5;

    var ax = a[0], ay = a[1], az = a[2], aw = a[3],
        by = Math.sin(rad), bw = Math.cos(rad);

    out[0] = ax * bw - az * by;
    out[1] = ay * bw + aw * by;
    out[2] = az * bw + ax * by;
    out[3] = aw * bw - ay * by;
    return out;
};

/**
 * Rotates a quaternion by the given angle about the Z axis
 *
 * @param {quat} out quat receiving operation result
 * @param {quat} a quat to rotate
 * @param {number} rad angle (in radians) to rotate
 * @returns {quat} out
 */
quat.rotateZ = function (out, a, rad) {
    rad *= 0.5;

    var ax = a[0], ay = a[1], az = a[2], aw = a[3],
        bz = Math.sin(rad), bw = Math.cos(rad);

    out[0] = ax * bw + ay * bz;
    out[1] = ay * bw - ax * bz;
    out[2] = az * bw + aw * bz;
    out[3] = aw * bw - az * bz;
    return out;
};

/**
 * Calculates the W component of a quat from the X, Y, and Z components.
 * Assumes that quaternion is 1 unit in length.
 * Any existing W component will be ignored.
 *
 * @param {quat} out the receiving quaternion
 * @param {quat} a quat to calculate W component of
 * @returns {quat} out
 */
quat.calculateW = function (out, a) {
    var x = a[0], y = a[1], z = a[2];

    out[0] = x;
    out[1] = y;
    out[2] = z;
    out[3] = Math.sqrt(Math.abs(1.0 - x * x - y * y - z * z));
    return out;
};

/**
 * Calculates the dot product of two quat's
 *
 * @param {quat} a the first operand
 * @param {quat} b the second operand
 * @returns {Number} dot product of a and b
 * @function
 */
quat.dot = vec4.dot;

/**
 * Performs a linear interpolation between two quat's
 *
 * @param {quat} out the receiving quaternion
 * @param {quat} a the first operand
 * @param {quat} b the second operand
 * @param {Number} t interpolation amount between the two inputs
 * @returns {quat} out
 * @function
 */
quat.lerp = vec4.lerp;

/**
 * Performs a spherical linear interpolation between two quat
 *
 * @param {quat} out the receiving quaternion
 * @param {quat} a the first operand
 * @param {quat} b the second operand
 * @param {Number} t interpolation amount between the two inputs
 * @returns {quat} out
 */
quat.slerp = function (out, a, b, t) {
    // benchmarks:
    //    http://jsperf.com/quaternion-slerp-implementations

    var ax = a[0], ay = a[1], az = a[2], aw = a[3],
        bx = b[0], by = b[1], bz = b[2], bw = b[3];

    var        omega, cosom, sinom, scale0, scale1;

    // calc cosine
    cosom = ax * bx + ay * by + az * bz + aw * bw;
    // adjust signs (if necessary)
    if ( cosom < 0.0 ) {
        cosom = -cosom;
        bx = - bx;
        by = - by;
        bz = - bz;
        bw = - bw;
    }
    // calculate coefficients
    if ( (1.0 - cosom) > 0.000001 ) {
        // standard case (slerp)
        omega  = Math.acos(cosom);
        sinom  = Math.sin(omega);
        scale0 = Math.sin((1.0 - t) * omega) / sinom;
        scale1 = Math.sin(t * omega) / sinom;
    } else {
        // "from" and "to" quaternions are very close
        //  ... so we can do a linear interpolation
        scale0 = 1.0 - t;
        scale1 = t;
    }
    // calculate final values
    out[0] = scale0 * ax + scale1 * bx;
    out[1] = scale0 * ay + scale1 * by;
    out[2] = scale0 * az + scale1 * bz;
    out[3] = scale0 * aw + scale1 * bw;

    return out;
};

/**
 * Calculates the inverse of a quat
 *
 * @param {quat} out the receiving quaternion
 * @param {quat} a quat to calculate inverse of
 * @returns {quat} out
 */
quat.invert = function(out, a) {
    var a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3],
        dot = a0*a0 + a1*a1 + a2*a2 + a3*a3,
        invDot = dot ? 1.0/dot : 0;

    // TODO: Would be faster to return [0,0,0,0] immediately if dot == 0

    out[0] = -a0*invDot;
    out[1] = -a1*invDot;
    out[2] = -a2*invDot;
    out[3] = a3*invDot;
    return out;
};

/**
 * Calculates the conjugate of a quat
 * If the quaternion is normalized, this function is faster than quat.inverse and produces the same result.
 *
 * @param {quat} out the receiving quaternion
 * @param {quat} a quat to calculate conjugate of
 * @returns {quat} out
 */
quat.conjugate = function (out, a) {
    out[0] = -a[0];
    out[1] = -a[1];
    out[2] = -a[2];
    out[3] = a[3];
    return out;
};

/**
 * Calculates the length of a quat
 *
 * @param {quat} a vector to calculate length of
 * @returns {Number} length of a
 * @function
 */
quat.length = vec4.length;

/**
 * Alias for {@link quat.length}
 * @function
 */
quat.len = quat.length;

/**
 * Calculates the squared length of a quat
 *
 * @param {quat} a vector to calculate squared length of
 * @returns {Number} squared length of a
 * @function
 */
quat.squaredLength = vec4.squaredLength;

/**
 * Alias for {@link quat.squaredLength}
 * @function
 */
quat.sqrLen = quat.squaredLength;

/**
 * Normalize a quat
 *
 * @param {quat} out the receiving quaternion
 * @param {quat} a quaternion to normalize
 * @returns {quat} out
 * @function
 */
quat.normalize = vec4.normalize;

/**
 * Creates a quaternion from the given 3x3 rotation matrix.
 *
 * NOTE: The resultant quaternion is not normalized, so you should be sure
 * to renormalize the quaternion yourself where necessary.
 *
 * @param {quat} out the receiving quaternion
 * @param {mat3} m rotation matrix
 * @returns {quat} out
 * @function
 */
quat.fromMat3 = function(out, m) {
    // Algorithm in Ken Shoemake's article in 1987 SIGGRAPH course notes
    // article "Quaternion Calculus and Fast Animation".
    var fTrace = m[0] + m[4] + m[8];
    var fRoot;

    if ( fTrace > 0.0 ) {
        // |w| > 1/2, may as well choose w > 1/2
        fRoot = Math.sqrt(fTrace + 1.0);  // 2w
        out[3] = 0.5 * fRoot;
        fRoot = 0.5/fRoot;  // 1/(4w)
        out[0] = (m[5]-m[7])*fRoot;
        out[1] = (m[6]-m[2])*fRoot;
        out[2] = (m[1]-m[3])*fRoot;
    } else {
        // |w| <= 1/2
        var i = 0;
        if ( m[4] > m[0] )
          i = 1;
        if ( m[8] > m[i*3+i] )
          i = 2;
        var j = (i+1)%3;
        var k = (i+2)%3;

        fRoot = Math.sqrt(m[i*3+i]-m[j*3+j]-m[k*3+k] + 1.0);
        out[i] = 0.5 * fRoot;
        fRoot = 0.5 / fRoot;
        out[3] = (m[j*3+k] - m[k*3+j]) * fRoot;
        out[j] = (m[j*3+i] + m[i*3+j]) * fRoot;
        out[k] = (m[k*3+i] + m[i*3+k]) * fRoot;
    }

    return out;
};

export default quat;
